Absolutely! Alignment is tremendously important if you want to hit consistent and accurate shots. I think your little experminent during practice has shown that. Alignment not only affects whether you hit the ball left or right but it can also determine whether you hit a draw/hook or a fade/slice. You need to ensure that your pre-shot routine includes some careful alignment checks. Personally my pre-shot routine is as follows:

1) Stand well behind the ball and set myself a target in the background. I've tried intermediate targets too but that doesn't work for me.

2) Place my clubhead behind the ball in line with the target

3) Align my body along the same line and lift the cluhbead away (I find this helps me set a good spine anlge)

4) Look at the target to check I'm lined up well (if I'm not I step away and start again!)

5) Make a few small adjustments to ensure I'm comfortable and then initiate the swing.

This routine may not work for you but it may help you to develop your own to help your alignment.